Australian mining magnate Gina Rinehart has reduced her stake in Fairfax Media, publisher of the Sydney Morning Herald and the Age newspapers, less than three weeks after she increased her investment in the group.

Minutes after the close of trade on the Australian stock market on Thursday, Rinehart sold 3.7% of the business to a major Australian fund manager, reducing her ownership in Fairfax Media to 15%.

The 86.5m shares sold were worth A$50.1m (£33.0m). Rinehart remains the largest shareholder.

A statement by Rinehart's company, Hancock Prospecting, said that the sale was completed to "esolve an issue that arose concerning the directors and officers insurance policy, in the situation of a director having a greater than 15% shareholding in Fairfax.

"This was one of the key issues recently raised by the chairman of Fairfax and needed to be resolved by either the chairman authorising endeavours to raise the 15% limit, which has been able to be reasonably achieved by other companies, or, as also discussed with the chairman, by sale of shares so that the largest shareholder had less than 15%," said the statement by chief development officer, John Klepec.

Last Monday, Rinehart threatened to sell her Fairfax shares if board seats were not made available to her without unsuitable conditions, a reference to the editorial charter of independence that has been at the centre of a row between her and the board.

Last week the board rejected her bid for three seats, citing her reluctance to accept the charter. Rinehart called on the chairman of Fairfax to increase the share price by more than 30% by November or resign.

In the statement that accompanied Thursday's sell-off, Rinehart reiterated her demand for the chairman to improve the share price or leave.

"We again urge the chairman to tell concerned shareholders that he will accept proposed milestones regarding his performance in the interests of Fairfax and its shareholders, or propose other reasonable KPIs [key performance indicators] to meet for the continuance of his chairmanship past the AGM in November 2012."

The continued sniping between Rinehart and the board comes after three weeks of major upheavals at Fairfax, during which the company announced it was cutting 1,900 jobs, converting its two flagship mastheads from broadsheets to tabloids, and closing its two main printing presses.

In another development, the Australian Financial Review – published by Fairfax – reports that the Fairfax chief executive, Greg Hywood, has attacked Rupert Murdoch's News Limited for creating a climate of distrust for the industry that has led to the Australian government planning to introduce a public interest test for media mergers and acquisitions.

Hywood refused to sign a letter to the government, co-authored by News Ltd chief executive Kim Williams, calling for any plans to introduce a public interest test to be scrapped.

"We're not about to sign a form letter penned by News Ltd to deal with the problem it created for the media industry in this country," Hywood said.

"We have our own views which will be expressed to the government … we will do it on the basis that it is at Fairfax, not News Ltd, that stands for editorial independence in this market and everybody knows it."

The Australian cabinet will consider the public interest test in about six weeks' time.

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